Partial-response signaling allows a better handling of intersymbol interference and allows a more efficient utilization of the bandwidth of a given channel. In partial-response (PR) systems a controlled amount of intersymbol interference can be allowed. As the intersymbol interference then is known, the receiver can take it into account. PR signaling in communications allows transmissions at the Nyquist rate, and provides an attractive trade-off between error probability and the available spectrum. The partial-response systems described by the polynomials 1+d, 1-d, and 1-d.sup.2 are also called duobinary, dicode, and class-IV, respectively.
Maximum-likelihood sequence estimation, in particular the Viterbi algorithm, is an effective tool in receivers for improving the detection of symbol sequences in the presence of intersymbol interference. It was described in the articles by G. D. Forney, "The Viterbi Algorithm," Proceedings of the IEEE, Vol. 61, No. 3, March 1973, pp. 268-278, and by G. Ungerbock, "Adaptive Maximum-likelihood Receiver for Carrier-modulated Data Transmission Systems", IEEE Transactions on Communications, Vol. COM-22, No. 5, May 1974, pp. 624-636. These articles also show some basic form of MLSE receivers or portions thereof.
The utilizaton of MLSE or Viterbi Algorithm in connection with partial-response signaling systems was already suggested for both above-mentioned application areas by publications of H. Kobayashi, "Application of Probabilistic Decoding to Digital Magnetic Recording Systems", IBM Journal of Research and Development, Vol. 15, No. 1, January 1971, pp. 64-74.
The problem of maximum-likelihood sequence estimation can be stated as follows. Given a received sequence (z.sub.n), where n is an integer time index, choose from among all possible transmitted sequences (x.sub.n) the one which is most likely to cause (z.sub.n) to be received, i.e. choose (x.sub.n) to maximize p((z.sub.n)/(x.sub.n)). The symbols of (x.sub.n) are not detected independently of one another, rather they are detected "in context". Maximum likelihood sequence estimation can be done efficiently using the Viterbi algorithm, a form of dynamic programming. The Viterbi algorithm maintains a set of "survivor" sequences and a metric for each indicating the likelihood of that sequence. One property of these metrics is that their absolute values can grow without bound.